随机网络上的分布式检测：大偏差性能分析
Distributed Detection over Random Networks: Large Deviations Performance Analysis
摘要：
我们研究了大偏差性能，即，随机网络上分布式检测算法的错误概率的指数衰减率。在每个时间步长$k$，每个传感器：1）将其决策变量与邻居的决策变量进行平均;以及2）在运行中考虑其新的观测。我们发现，分布式检测表现出“相变”的行为。当网络信息流的速率（平均化的速度）高于阈值时，则分布式检测渐进地等价于最优集中式检测，即，分布式检测的错误概率的指数衰减率等于DADFF信息。当信息流的速率低于阈值时，分布式检测仅实现了一小部分的Wuff信息速率;我们将此可实现的速率量化为信息流的网络速率的函数。仿真例子证明了我们的理论研究结果的行为分布检测随机网络。
英文摘要：
We study the large deviations performance, i.e., the exponential decay rate of the error probability, of distributed detection algorithms over random networks. At each time step $k$ each sensor: 1) averages its decision variable with the neighbors' decision variables; and 2) accounts on-the-fly for its new observation. We show that distributed detection exhibits a "phase change" behavior. When the rate of network information flow (the speed of averaging) is above a threshold, then distributed detection is asymptotically equivalent to the optimal centralized detection, i.e., the exponential decay rate of the error probability for distributed detection equals the Chernoff information. When the rate of information flow is below a threshold, distributed detection achieves only a fraction of the Chernoff information rate; we quantify this achievable rate as a function of the network rate of information flow. Simulation examples demonstrate our theoretical findings on the behavior of distributed detection over random networks.
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